[EM] Voting by selecting a published ordering (was sidetracked to EC)

[Steve Eppley]

Hi,

Forest S wrote:
> Steve E. wrote:
 >-snip-
>> Now... can we please go back to discussing whether candidates would have sufficiently
>> strong incentives to rank compromise candidates over worse candidates, when
>> publishing their orderings before election day, assuming the voting method I repeated
>> above?
> 
> Yes!  In your scenario of 
 >    35M  Bush>McCain>Gore
 >    20M  McCain>Bush>Gore
 >    45M  Gore>McCain>Bush
> 
> Suppose Rove saw this coming, and not relying completely on slandering McCain this
> time, decided to publish the Bush ranking as
> 
> Bush>Gore>McCain
> 
> Wouldn't it be to McCain's advantage to fail to rank the other two candidates?

Perhaps.  McCain looks like the sincere Condorcet winner here. (I believe he was the 
sincere Condorcet winner in 2000, by the way.)  Some voting methods satisfy the Minimal 
Defense criterion, in which the supporters of the sincere Condorcet winner can induce an 
equilibrium that elects him/her by omitting less preferred candidates from their 
orderings. (MAM satisfies Minimal Defense.)  There's an obvious analogy; in this example 
the ordering published by the sincere Condorcet winner omits the less preferred 
candidates.  I don't believe this behavior by a sincere Condorcet winner would be a 
problem.  My question was more specifically whether there would be sufficiently strong 
incentives for Gore to choose to rank McCain over Bush, even though McCain is not a member 
of Gore's party.  If candidates will behave that way, then this simple voting method is 
quite worthy of promotion.

I specified a tallying method I hoped would be considered first when considering the 
example: allowing candidates to withdraw after the votes are cast and then counting each 
ordering for its topmost non-withdrawn candidate. (In other words, Plurality Rule.)  Of 
course, you're all free to discuss any tallying method you please.

Although the Gore/McCain/Bush example uses the names of candidates from a recent 
Presidential election, I didn't write that they're running for President.  My purpose in 
using those names was because I expected the readers would be familiar with their party 
affiliations and the voters' relative preferences about them in 2000, not because I expect 
we can reform the voting method used in Presidential elections any time soon.  Reforming 
less important elections must come first, to demonstrate to the public the desirability of 
the new method(s). (This is another reason why I consider our recent discussion of the 
Electoral College to have gotten us temporarily off track.)  I'm wondering now if it would 
have been more helpful if I'd chosen an example without recognizable names, such as the 
following:

    Three candidates R1, R2 and D competing for a seat in
    some state's Senate or Assembly.

    The voters' top choices:
       35% prefer R1.
       20% prefer R2.
       45% prefer D.

    The candidates' sincere preference orders:
       R1:  R1 > R2 > D
       R2:  R2 > R1 > D
       D:   D  > R2 > R1

    Assume that nearly all of the 35% who prefer R1 also
    prefer R2 over D, and that nearly all of the 45% who
    prefer D also prefer R2 over R1.  The 20% who prefer
    R2 are divided about who is second best, with most
    of them preferring R1 over D.

Will D publish the ordering D > R2 > R1?

As a variation, assume the R party nominated R1 but not R2, and then R2 chose to continue 
competing as an independent candidate.  R2 need not worry about being a spoiler if s/he 
publishes the ordering R2>R1>D, since if necessary s/he can withdraw after the voting.  By 
running s/he'd most likely increase the voter turnout, making it harder for D to win. 
When considering this variation, we would also want to consider the cases where R1's 
sincere preference ordering is R1 > R2=D or R1 > D > R2.

Regards,
Steve